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Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains

Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains

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This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on.

In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. 

The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.

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This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on.

In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. 

The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.

Produktdetaljer
Sprog: Engelsk
Sider: 399
ISBN-13: 9783030653743
Indbinding: Paperback
Udgave:
ISBN-10: 3030653749
Udg. Dato: 2 apr 2022
Længde: 0mm
Bredde: 155mm
Højde: 235mm
Forlag: Springer Nature Switzerland AG
Oplagsdato: 2 apr 2022
Forfatter(e) Oleg Sarafanov, Boris Plamenevskii, Dmitrii Korikov


Kategori Differentialregning & ligninger


ISBN-13 9783030653743


Sprog Engelsk


Indbinding Paperback


Sider 399


Udgave


Længde 0mm


Bredde 155mm


Højde 235mm


Udg. Dato 2 apr 2022


Oplagsdato 2 apr 2022


Forlag Springer Nature Switzerland AG

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